Cottrell Boyce, who wrote the opening ceremony for London 2012, said he was "flabbergasted" to be invited to work on the show.
The episode, to be screened later this year, features a cast of young actors including Harley Bird, who landed a Bafta for voicings animated character Peppa, as well as Abigail Eames who featured in The Crimson Field, Ashley Foster from the The Woman In Black and Jaydon Harris-Wallace.
Cottrell Boyce's films have included 24 Hour Party People, about the Manchester music scene, and the Danny Boyle-directed Millions.
He said: "Of all the thrills that pen and paper have brought into my life, there's nothing that quite compares to the buzz of unlimited possibility that rushes through your fingers and into your brain when you write the words 'Interior: Tardis'.
"I was flabbergasted to be asked to write an episode - partly because I've been so absorbed in the last few series that I'd sort of forgotten that it wasn't real."
Doctor Who's executive producer Steven Moffat said: "Frank's script is pure magic - and everything I could have hoped for from the genius behind the Olympics opening ceremony. Doctor Who is born anew in the mind of a genius."
The series returns to BBC1 on August 23 with Peter Capaldi starring as The Doctor.